Question
- Define self inductance. Write its S.I. units.
- Derive an expression for self inductance of a long, solenoid of length l, cross sectional area A having N number of turns.
Alternate Answer
It is the emf induced in the coil when the rate of change of current through it is unity.
SI Unit is henry
The magnetic field due to a current I flowing in the solenoid is B =µ0nI The total flux linked with the solenoid is NBA, i.e.
$\phi =\big(\text{nl}\big)\big(\mu_\circ\text{nI}\big)\text{A}$
$ = \mu_\circ\text{n}^{2}\ \text{IlA}$
$\text{L} =\frac{\phi}{\text{I}} =\mu_\circ\text{n}^{2} \text{Al}$
$ = \frac{\mu_\circ\text{N}^{2}\text{A}}{l}$
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